On Fri, Oct 3, 2008 at 11:12 AM, Waldek Hebisch wrote:
>
> Bill Page wrote:
>> 1) Use of coercions and types in InputForm.
>> ...
>> One alternative would be to introduce a specific (non-overloaded)
>> operation exported by AlgebraicNumber such as 'algebraicNumber'
>> that does the same thing. That is how Float values are currently
>> handled:
>>
>> (8) -> 3.141592::InputForm
>>
>> (8) (float 231808574432053350722 - 66 2)
>> Type: InputForm
>> (9) -> unparse %
>>
>> (9) "float(231808574432053350722,-66,2)"
>> Type: String
>>
>> Would doing something like this:
>>
>> (algebraicNumber (** 2 (/ 1 2)))
>>
>> be better?
>>
>
> What is type of argument to this hypotethical function?
algebraicNumber:Expression Integer -> AlgebraicNumber
> AFAICS constructing floats works well because float can be
> reconstructed from few integers.
I am concerned that the definition and use of coercion to InputForm is
not very clear in panAxiom. I believe the main purpose is to provide a
convenient means in each domain to express domain values as easily
evaluated expressions. It seems to me that there is always a general
solution to this problem that is based on the representation Rep of
the domain. For example, for any domain MyDomain
if Rep has CoercibleTo(InputForm) then
coerce(x:%) :InputForm ==
convert(['myDomain,coerce(rep x)@InputForm])
myDomain(x:Rep):% == per x
To make this work in general we also need standard coercions to
InputForm for built-in constructors like Record. For the most part
these already exist. For example we need something like this: For any
Record(a:A,b:B, ... ):
if A has CoercibleTo(InputForm) and
B has CoercibleTo(InputForm) ... then
coerce(x:%):InputForm ==
convert(['construct,convert([coerce(rep(x).a)@InputForm,
coerce(rep(x).a)@InputForm, ... ]) ])
In the case of Float the Rep is
Rep := Record( mantissa:Interger, exponent:Integer )
So for '3.141592::InputForm' we would get:
(float (construct (231808574432053350722 -66)))
or unparse
float(construct(231808574432053350722, -66))
This is essentially what is implemented for Float except that the
'construct' operator is absorbed into 'float' and the 3rd argument is
gratuitous.
> But for algebraic numbers we need much more complicated construction:
> in general we need to specify tower of algebraic extensions.
I don't think so. The same general construction can be applied as
above. The Rep of AlgebraicNumber is Expression(Integer).
>
>> 2) Notice that the InputForm value representing the same expression
>> occur with both ** and ^. Which one is currently the preferred form?
>>
>
> ^ is the preferred form. ** will be eliminated.
>
Ok, I will change my patch to reflect this. Thanks.
Regards,
Bill Page.
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